Factor completely. $3x^5-75x^3=$
Solution: As a first step, let's see if there's a common factor we can factor out. Greatest common factor The greatest common factor of $3x^5$ and $-75x^3$ is $3x^3$. Let's factor $3x^3$ out of $3x^5-75x^3$ : $\begin{aligned} &\phantom{=}3x^5-75x^3 \\\\ &=3x^3(x^2)+3x^3(-25) \\\\ &=3x^3(x^2-25) \end{aligned}$ We can keep factoring the expression by factoring $x^2-25$. Factoring $x^2-25$ We notice this expression has the difference of squares pattern: $\begin{aligned} &\phantom{=}x^2-25 \\\\ &=(x)^2-(5)^2 \\\\ &=(x+5)(x-5) \end{aligned}$ Putting it all together $\begin{aligned} &\phantom{=}3x^5-75x^3 \\\\ &=3x^3(x^2-25) \\\\ &=3x^3(x+5)(x-5) \end{aligned}$ In conclusion, this is the completely factored expression: $3x^3(x+5)(x-5)$